My primary area of research is Distributed Matrix Algebra, which is also the domain of my doctoral thesis. However, I also have been working on Music Information Retrieval and Computational Musicology, the research area during my master’s degree, for the last couple of years.
The primary objective of my Ph.D. research was to accelerate the process of creating interpolated surfaces from large scale spatial dataset for compute resource demanding spatial interpolation techniques (Ordinary Kriging in this case) on Big Data platform (Apache Spark in this case). Solution of Ordinary Kriging equation requires solving n linear equations, formed from n interpolating points, for each of m prediction points i.e. a running time of...
O(mn^3). Since Apache Spark on a high level operates on map and reduce based programming constructs, the traditional way of solving linear equations (i.e. using matrix decomposition, forward substitutions and backward eliminations) is not suitable for acceleration (forming long graphs of basic data abstraction). Instead the problem at hand had been solved using a matrix inversion and a matrix-matrix multiplication using distributed block-recursive approaches. For matrix inversion we have used a less explored method given by Strassen in his famous 1969 matrix multiplication paper and the Spark based parallel implementation, SPIN, of the algorithm was very effective.
Developing a faster algorithm for matrix-matrix multiplication was challenging as there are already an ample number of robust algorithms, the state-of-the-art MLLIB (Spark multiplication routine) was one of the contestants. However, the novelty of our algorithm, STARK, was to process the Strassen’s multiplication recursive tree in a BFS way and parallelize the computation for each such recursion level at once. This has been accomplished by tagging the submatrices dynamically at each level and distributing them to the nodes so that computations can be done locally. These two works accelerate the overall Kriging computation and finally we get a faster algorithm.
While the above two algorithms were fast they are constrained with the nature of the matrix. We noticed that the running time could be reduced substantially by considering symmetric positive definiteness for inversion (Kriging covariance matrix) and rectangular matrix for multiplication. This resulted in a faster distributed block recursive cholesky based inversion algorithm and a faster distributed rectangular Strassen’s algorithm which used zero padding technique for multiplication.
Two important research directions emerged from my thesis as a future work - distributed algorithms for sparse matrices and distributed approximation algorithms for matrix computations. Currently, I am focusing on sparse matrix representation for efficient storage in memory is a constraint, edge ...
devices for example. After the completion of my Ph.D. I am once again revisiting my old passion in Sound and Music Computing at XIM University and I have published three research papers in this domain since 2021. These publications are my initial attempts towards a larger research eco-system that requires attention from Indian scholars to expand the knowledge base on state-of-the-art tools for research in Indic music.